indefinite-integration

Question: Let $f(x)=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})\,\left( 1+\sqrt{1+{{x}^{2}}} \right)}}$and $f(0)=0$, then the value of $f(1)$ be

1) $\log (1+\sqrt{2})$

2) $\log (1+\sqrt{2})-\frac{\pi }{4}$

3) $\log (1+\sqrt{2})+\frac{\pi }{2}$

4) None of these

Solution:

Explanation: No Explanation

Integration by substitution

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